{"paper":{"title":"Tractability of multivariate analytic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, Henryk Wozniakowski, Peter Kritzer","submitted_at":"2014-07-07T08:15:03Z","abstract_excerpt":"In the theory of tractability of multivariate problems one usually studies problems with finite smoothness. Then we want to know which $s$-variate problems can be approximated to within $\\varepsilon$ by using, say, polynomially many in $s$ and $\\varepsilon^{-1}$ function values or arbitrary linear functionals.\n  There is a recent stream of work for multivariate analytic problems for which we want to answer the usual tractability questions with $\\varepsilon^{-1}$ replaced by $1+\\log \\varepsilon^{-1}$. In this vein of research, multivariate integration and approximation have been studied over Ko"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1615","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}